The emergence in recent years of a powerful “double copy” relation between
gravitational and gauge theory scattering amplitudes
[1]}, [2]}, mirroring earlier such relations found in
string theory [3]}, has led to a wide variety of applications,
including the ability to calculate higher-loop supergravity amplitudes and
in gravitational wave physics (see [4]} and references cited
therein). Given the by now well-established double copy relation for
scattering amplitudes, a clear question worth pursuing is whether this
relation is reflected at the level of classical solutions
(see [5]} and references cited therein). Most of the
explicit such relationships that have been found, such that the Kerr-Schild
double copy [6]} or the Weyl double copy
[7]}, work for a special class of gravitational solutions.
However, the convolutional double copy
[8]}, [9]}, [10]} posits a square relationship
between gauge and gravitational theories at the level of the fields,
albeit at the linearised level. We shall be focusing on this approach in
this paper.
